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Mirrors > Home > ILE Home > Th. List > sbhypf | Unicode version |
Description: Introduce an explicit substitution into an implicit substitution hypothesis. See also csbhypf . (Contributed by Raph Levien, 10-Apr-2004.) |
Ref | Expression |
---|---|
sbhypf.1 |
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sbhypf.2 |
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Ref | Expression |
---|---|
sbhypf |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | vex 2692 |
. . 3
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2 | eqeq1 2147 |
. . 3
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3 | 1, 2 | ceqsexv 2728 |
. 2
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4 | nfs1v 1913 |
. . . 4
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5 | sbhypf.1 |
. . . 4
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6 | 4, 5 | nfbi 1569 |
. . 3
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7 | sbequ12 1745 |
. . . . 5
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8 | 7 | bicomd 140 |
. . . 4
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9 | sbhypf.2 |
. . . 4
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10 | 8, 9 | sylan9bb 458 |
. . 3
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11 | 6, 10 | exlimi 1574 |
. 2
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12 | 3, 11 | sylbir 134 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-5 1424 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-8 1483 ax-11 1485 ax-4 1488 ax-17 1507 ax-i9 1511 ax-ial 1515 ax-i5r 1516 ax-ext 2122 |
This theorem depends on definitions: df-bi 116 df-tru 1335 df-nf 1438 df-sb 1737 df-clab 2127 df-cleq 2133 df-clel 2136 df-v 2691 |
This theorem is referenced by: mob2 2868 cbvmptf 4030 tfisi 4509 ralxpf 4693 rexxpf 4694 nn0ind-raph 9192 |
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